Title: Virtuality Distributions in application to gamma gamma* to pi^0 Transition Form Factor at Handbag Level

We outline basics of a new approach to transverse momentum dependence in hard processes. As an illustration, we consider hard exclusive transition process gamma*gamma -> to pi^0 at the handbag level. Our starting point is coordinate representation for matrix elements of operators (in the simplest case, bilocal O(0,z)) describing a hadron with momentum p. Treated as functions of (pz) and z^2, they are parametrized through a virtuality distribution amplitude (VDA) Phi (x, sigma), with x being Fourier-conjugate to (pz) and sigma Laplace-conjugate to z^2. For intervals with z^+=0, we introduce transverse momentum distribution amplitude (TMDA) Psi (x, k_\perp), and write it in terms of VDA Phi (x, \sigma). The results of covariant calculations, written in terms of Phi (x sigma) are converted into expressions involving Psi (x, k_\perp. Starting with scalar toy models, we extend the analysis onto the case of spin-1/2 quarks and QCD. We propose simple models for soft VDAs/TMDAs, and use them for comparison of handbag results with experimental (BaBar and BELLE) data on the pion transition form factor. We also discuss how one can generate high-k_\perp tails from primordial soft distributions.